I can ride no hands and do from time to time to just stretch, mostly near the end of a ride. I do it to grab stuff out of back pockets and mess with whatever it is I get, such as food that needs wrappers taken off and what not. Zipping up jerseys or jackets.
I look backwards as well but I sometime will look under my arm when on/in the drops. I can look about halfway and like Hermes said use peripheral vision by just turning head . A lot of the time I will take one hand off bar and turn body around and put free hand on seat to get a real good look like when I have to cross a street to make a left turn and need to see a ways back for oncoming traffic.